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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 6.3, Problem 16E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Using the Trapezoidal Rule and Simpson’s Rule In Exercises 11-20, approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of n. Round your answers to three decimal places. See Examples 1 and 2.

∫ 0 2 e − x 2 d x , n = 4

(a)

To determine

To calculation: The value of the integral ∫02e−x2dx,n=4 by using the Trapezoidal Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

Explanation

Given Information:

The definite integral is ∫02e−x2dx,n=4

Formula used:

Trapezoidal Rule:

If a function f is continuous on [a,b], then

∫abf(x)dx≈(b−a2n)[f(x0)+2f(x0)+...+2f(xn−1)+f(xn)]

Calculation:

Calculation by Trapezoidal Rule:

Consider the definite integral ∫02e−x2dx,n=4.

When n=4, the width of each subinterval is

2−04=24=12

And the end points of subintervals are

x0=0x1=12x2=1

And,

x3=32x4=2

The graph of the function is for interval,

(b)

To determine

To calculation: The value of the integral ∫02e−x2dx,n=4 by using the Simpson’s Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

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Sect-6.1 P-1CPSect-6.1 P-2CPSect-6.1 P-3CPSect-6.1 P-4CPSect-6.1 P-5CPSect-6.1 P-6CPSect-6.1 P-7CPSect-6.1 P-1SWUSect-6.1 P-2SWUSect-6.1 P-3SWU
Sect-6.1 P-4SWUSect-6.1 P-5SWUSect-6.1 P-6SWUSect-6.1 P-7SWUSect-6.1 P-8SWUSect-6.1 P-9SWUSect-6.1 P-10SWUSect-6.1 P-1ESect-6.1 P-2ESect-6.1 P-3ESect-6.1 P-4ESect-6.1 P-5ESect-6.1 P-6ESect-6.1 P-7ESect-6.1 P-8ESect-6.1 P-9ESect-6.1 P-10ESect-6.1 P-11ESect-6.1 P-12ESect-6.1 P-13ESect-6.1 P-14ESect-6.1 P-15ESect-6.1 P-16ESect-6.1 P-17ESect-6.1 P-18ESect-6.1 P-19ESect-6.1 P-20ESect-6.1 P-21ESect-6.1 P-22ESect-6.1 P-23ESect-6.1 P-24ESect-6.1 P-25ESect-6.1 P-26ESect-6.1 P-27ESect-6.1 P-28ESect-6.1 P-29ESect-6.1 P-30ESect-6.1 P-31ESect-6.1 P-32ESect-6.1 P-33ESect-6.1 P-34ESect-6.1 P-35ESect-6.1 P-36ESect-6.1 P-37ESect-6.1 P-38ESect-6.1 P-39ESect-6.1 P-40ESect-6.1 P-41ESect-6.1 P-42ESect-6.1 P-43ESect-6.1 P-44ESect-6.1 P-45ESect-6.1 P-46ESect-6.1 P-47ESect-6.1 P-48ESect-6.1 P-49ESect-6.1 P-50ESect-6.1 P-51ESect-6.1 P-52ESect-6.1 P-53ESect-6.1 P-54ESect-6.1 P-55ESect-6.1 P-56ESect-6.1 P-57ESect-6.1 P-58ESect-6.1 P-59ESect-6.1 P-60ESect-6.1 P-61ESect-6.1 P-62ESect-6.1 P-63ESect-6.1 P-64ESect-6.1 P-65ESect-6.1 P-66ESect-6.1 P-67ESect-6.1 P-68ESect-6.1 P-69ESect-6.1 P-70ESect-6.1 P-71ESect-6.1 P-72ESect-6.1 P-73ESect-6.1 P-74ESect-6.1 P-75ESect-6.1 P-76ESect-6.1 P-77ESect-6.1 P-78ESect-6.1 P-79ESect-6.1 P-80ESect-6.1 P-81ESect-6.1 P-82ESect-6.2 P-1CPSect-6.2 P-2CPSect-6.2 P-3CPSect-6.2 P-4CPSect-6.2 P-5CPSect-6.2 P-6CPSect-6.2 P-1SWUSect-6.2 P-2SWUSect-6.2 P-3SWUSect-6.2 P-4SWUSect-6.2 P-5SWUSect-6.2 P-6SWUSect-6.2 P-1ESect-6.2 P-2ESect-6.2 P-3ESect-6.2 P-4ESect-6.2 P-5ESect-6.2 P-6ESect-6.2 P-7ESect-6.2 P-8ESect-6.2 P-9ESect-6.2 P-10ESect-6.2 P-11ESect-6.2 P-12ESect-6.2 P-13ESect-6.2 P-14ESect-6.2 P-15ESect-6.2 P-16ESect-6.2 P-17ESect-6.2 P-18ESect-6.2 P-19ESect-6.2 P-20ESect-6.2 P-21ESect-6.2 P-22ESect-6.2 P-23ESect-6.2 P-24ESect-6.2 P-25ESect-6.2 P-26ESect-6.2 P-27ESect-6.2 P-28ESect-6.2 P-29ESect-6.2 P-30ESect-6.2 P-31ESect-6.2 P-32ESect-6.2 P-33ESect-6.2 P-34ESect-6.2 P-35ESect-6.2 P-36ESect-6.2 P-37ESect-6.2 P-38ESect-6.2 P-39ESect-6.2 P-40ESect-6.2 P-41ESect-6.2 P-42ESect-6.2 P-43ESect-6.2 P-44ESect-6.2 P-45ESect-6.2 P-46ESect-6.2 P-47ESect-6.2 P-48ESect-6.2 P-49ESect-6.2 P-50ESect-6.2 P-51ESect-6.2 P-52ESect-6.2 P-53ESect-6.2 P-54ESect-6.2 P-55ESect-6.2 P-56ESect-6.2 P-57ESect-6.2 P-58ESect-6.2 P-59ESect-6.2 P-60ESect-6.2 P-61ESect-6.2 P-1QYSect-6.2 P-2QYSect-6.2 P-3QYSect-6.2 P-4QYSect-6.2 P-5QYSect-6.2 P-6QYSect-6.2 P-7QYSect-6.2 P-8QYSect-6.2 P-9QYSect-6.2 P-10QYSect-6.2 P-11QYSect-6.2 P-12QYSect-6.2 P-13QYSect-6.2 P-14QYSect-6.2 P-15QYSect-6.2 P-16QYSect-6.2 P-17QYSect-6.2 P-18QYSect-6.2 P-19QYSect-6.2 P-20QYSect-6.2 P-21QYSect-6.3 P-1CPSect-6.3 P-2CPSect-6.3 P-3CPSect-6.3 P-1SWUSect-6.3 P-2SWUSect-6.3 P-3SWUSect-6.3 P-4SWUSect-6.3 P-5SWUSect-6.3 P-6SWUSect-6.3 P-7SWUSect-6.3 P-8SWUSect-6.3 P-9SWUSect-6.3 P-10SWUSect-6.3 P-1ESect-6.3 P-2ESect-6.3 P-3ESect-6.3 P-4ESect-6.3 P-5ESect-6.3 P-6ESect-6.3 P-7ESect-6.3 P-8ESect-6.3 P-9ESect-6.3 P-10ESect-6.3 P-11ESect-6.3 P-12ESect-6.3 P-13ESect-6.3 P-14ESect-6.3 P-15ESect-6.3 P-16ESect-6.3 P-17ESect-6.3 P-18ESect-6.3 P-19ESect-6.3 P-20ESect-6.3 P-31ESect-6.3 P-32ESect-6.3 P-33ESect-6.3 P-34ESect-6.3 P-35ESect-6.3 P-36ESect-6.3 P-37ESect-6.3 P-38ESect-6.3 P-39ESect-6.3 P-40ESect-6.3 P-43ESect-6.3 P-44ESect-6.3 P-45ESect-6.3 P-46ESect-6.3 P-47ESect-6.3 P-48ESect-6.4 P-1CPSect-6.4 P-2CPSect-6.4 P-3CPSect-6.4 P-4CPSect-6.4 P-5CPSect-6.4 P-1SWUSect-6.4 P-2SWUSect-6.4 P-3SWUSect-6.4 P-4SWUSect-6.4 P-5SWUSect-6.4 P-6SWUSect-6.4 P-7SWUSect-6.4 P-8SWUSect-6.4 P-9SWUSect-6.4 P-10SWUSect-6.4 P-1ESect-6.4 P-2ESect-6.4 P-3ESect-6.4 P-4ESect-6.4 P-5ESect-6.4 P-6ESect-6.4 P-7ESect-6.4 P-8ESect-6.4 P-9ESect-6.4 P-10ESect-6.4 P-11ESect-6.4 P-12ESect-6.4 P-13ESect-6.4 P-14ESect-6.4 P-15ESect-6.4 P-16ESect-6.4 P-17ESect-6.4 P-18ESect-6.4 P-19ESect-6.4 P-20ESect-6.4 P-21ESect-6.4 P-22ESect-6.4 P-23ESect-6.4 P-24ESect-6.4 P-25ESect-6.4 P-26ESect-6.4 P-27ESect-6.4 P-28ESect-6.4 P-29ESect-6.4 P-30ESect-6.4 P-31ESect-6.4 P-32ESect-6.4 P-33ESect-6.4 P-34ESect-6.4 P-35ESect-6.4 P-36ESect-6.4 P-37ESect-6.4 P-38ESect-6.4 P-39ESect-6.4 P-40ESect-6.4 P-41ESect-6.4 P-42ECh-6 P-1RECh-6 P-2RECh-6 P-3RECh-6 P-4RECh-6 P-5RECh-6 P-6RECh-6 P-7RECh-6 P-8RECh-6 P-9RECh-6 P-10RECh-6 P-11RECh-6 P-12RECh-6 P-13RECh-6 P-14RECh-6 P-15RECh-6 P-16RECh-6 P-17RECh-6 P-18RECh-6 P-19RECh-6 P-20RECh-6 P-21RECh-6 P-22RECh-6 P-23RECh-6 P-24RECh-6 P-25RECh-6 P-26RECh-6 P-27RECh-6 P-28RECh-6 P-29RECh-6 P-30RECh-6 P-31RECh-6 P-32RECh-6 P-33RECh-6 P-34RECh-6 P-35RECh-6 P-36RECh-6 P-37RECh-6 P-38RECh-6 P-39RECh-6 P-40RECh-6 P-41RECh-6 P-42RECh-6 P-43RECh-6 P-44RECh-6 P-45RECh-6 P-46RECh-6 P-47RECh-6 P-48RECh-6 P-49RECh-6 P-50RECh-6 P-51RECh-6 P-52RECh-6 P-53RECh-6 P-54RECh-6 P-55RECh-6 P-56RECh-6 P-57RECh-6 P-58RECh-6 P-59RECh-6 P-60RECh-6 P-61RECh-6 P-62RECh-6 P-63RECh-6 P-64RECh-6 P-1TYSCh-6 P-2TYSCh-6 P-3TYSCh-6 P-4TYSCh-6 P-5TYSCh-6 P-6TYSCh-6 P-7TYSCh-6 P-8TYSCh-6 P-9TYSCh-6 P-10TYSCh-6 P-11TYSCh-6 P-12TYSCh-6 P-13TYSCh-6 P-14TYSCh-6 P-15TYSCh-6 P-16TYSCh-6 P-17TYSCh-6 P-18TYS

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